Drag induced flow

Steady Drag-induced Flow in Straight Channels, 162... 

STEADY DRAG-INDUCED FLOW IN STRAIGHT CHANNELS... 

Drag-induced flow in a rectangular channel, as in Fig. 4.15, neglecting cross-channel forces, resulted in Eq. 4.9-3. We now consider the effect of these forces on the conveying mechanism. 

Removal of the melt, also discussed in Section 5.1, is made possible, in principle, by two mechanisms drag-induced flow and pressure-induced flow (Fig. 5.4). In both cases, the molten layer must be sheared, leading to viscous dissipation. The latter provides an additional, important source of thermal energy for melting, the rate of which can be controlled externally either by the velocity of the moving boundary in drag-induced melt removal or the external force applied to squeeze the solid onto the hot surface, in pressure-induced melt removal. 

Unlike in drag-induced flows, where we compute the flow rate from the velocity profiles, in this case, because of the positive displacement nature of the flow, we could easily relate flow rate to the axial motion of the closed chambers. But in order to understand the nature of the flow inside the chamber, for mixing and power consumption we do need to derive the detailed velocity profiles. 

It seems logical that because screw rotation causes drag-induced flow, a condition for good solids conveyance in this region would be high interaction (friction) between the solids and the screw. But, this is a case for counter intuition In fact, when there is high friction between the solids and screw, the solids stick to the screw and simply rotate around and around, never moving toward the die. 

To facilitate an understanding of how particulate solids are transported through a single-screw extruder we start with a model for drag-induced flow in straight channels. We then summarize the equations for flow of particulate solids in the single-screw extruder. We next add heat transfer to the transport of the particulate solids. 

The degradation ribbon at the merger of the flows occurs because of the crosschannel flow of material from the region between the solid bed and the screw root to the melt pool. As shown by Fig. 6.35, this flow is relatively large. As previously stated, the flow occurs because of pressure-induced flow and the dragging of fresh material under the solid bed by the backwards motion of the screw root. This process is consistent with the physics presented for screw rotation. The flow fields developed for a barrel rotation system would not create the low-flow region such as shown in Fig. 6.37. 

The unit can be fed polymer in the particulate solids form or as strips, as in the case of rubber extrusion. The solids (usually in pellet or powder form) in the hopper flow by gravity into the screw channel, where they are conveyed through the solids conveying section. They are compressed by a drag-induced mechanism in the transition section. In other words, melting is accomplished by heat transfer from the heated barrel surface and by mechanical shear heating. 

The steady and dynamic drag-induced simple shear-flow rheometers, which are limited to very small shear rates for the steady flow and to very small strains for the dynamic flow, enable us to evaluate rheological properties that can be related to the macromolecular structure of polymer melts. The reason is that very small sinusoidal strains and very low shear rates do not take macromolecular polymer melt conformations far away from their equilibrium condition. Thus, whatever is measured is the result of the response of not just a portion of the macromolecule, but the contribution of the entire macromolecule. 

Drag-induced pressurization in shallow screw channels was discussed in Section 6.3, and the flow rate is given in Eqs. 6.3-27 and 6.3-28. The former can be rewritten as... 

The dynamical evolution of solids in protoplanetary disks is controlled by the large-scale flows that develop due to disk evolution, diffusion associated with the turbulence that is related to disk evolution or shear instabilities, gas-drag-induced motions due to different orbital velocities of the gas and solids, and settling towards the mid-plane due to the vertical component of the central star s gravity. As the large-scale flows have already been discussed, we now discuss the other sources of particle motions. 

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